Questions: A boat begins at point A and heads straight across a 60-meter wide river with a speed of 4 m / s (relative to the water). The river water flows north at a speed of 3 m / s (relative to the shore). The boat reaches the opposite shore at point C. Which of the following would cause the boat to reach the opposite shore in MORE time? Include all that apply. a. The river flows north at 2 m / s. b. The river flows north at 4 m / s. c. The boat heads across the river at 3 m / s. d. The boat heads across the river at 5 m / s. e. The river is 40 meters wide. f. The river is 80 meters wide. g. Nonsense! None of these affect the time to cross the river.

Solution Steps

The boat's velocity component perpendicular to the river flow determines the time it takes to cross the river. The river flow velocity only affects where the boat lands on the opposite shore (point C).

The time it takes to cross the river is given by:

\(t = \frac{d}{v_{\perp}}\)

where \(d\) is the width of the river and \(v_{\perp}\) is the boat's speed component perpendicular to the river flow.

a. If the river flows north at 2 m/s, the time to cross remains unaffected. The boat's perpendicular velocity remains 4 m/s. b. If the river flows north at 4 m/s, the time to cross remains unaffected. The boat's perpendicular velocity remains 4 m/s. c. If the boat heads across the river at 3 m/s, the time to cross increases, as \(v_{\perp}\) decreases. d. If the boat heads across the river at 5 m/s, the time to cross decreases, as \(v_{\perp}\) increases. e. If the river is 40 meters wide, the time to cross decreases, as \(d\) decreases. f. If the river is 80 meters wide, the time to cross increases, as \(d\) increases. g. Incorrect. Options c, e, and f affect the time to cross the river.

Final Answer: